Can layers of deep neural networks be seen as Hopfield networks?
Deep Learning is not a generalization of Hopfield networks. Deep Learning is a &quot;generalization&quot; of the neural networks/connectionism field started by Rumelhart and McClelland.
There are two kinds of neural networks:

Directed (Perceptron, MLP, ConvNets, RNNs, etc.)
Undirected (Hopfield Nets, Boltzmann Machines, Energy-based models, etc.)

Any of these can be made deep. As you said, Boltzmann machines are the probabilistic version of Hopfield Networks, and there has been a lot more work on deepifying these models than Hopfield nets: Deep Boltzmann machines, Deep Belief Networks, and deep energy models. Hinton is really the guy you want to read to learn about these models, but you can have a look at this paper which compares the three models.
Not sure about the Gestalt organisation. I guess I'll leave that to your interpretation.